Multiplicative models of financial returns and what we fail to get when they are disregarded

This paper puts forward an alternative approach to multiplicative models and their assessment of returns out of financial assets. Firstly, it lays down an operative definition but also sets forth a commutative framework of mappings to provide foundations to such a definition. Next, the total return is split down into its linear and non-linear building blocks. Afterwards, a compatibility lemma draws a distinction between what should be meant by linear approximation and linear equivalence to the multiplicative model. Last of all, three empirical examples bring home how to profit from multiplicative models in actual practice.